Bit-wise Unequal Error Protection for Variable Length Block Codes with Feedback

The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures is used to establish inner bounds to the achievable performance for finite expected decoding time. A new technique for bounding the performance of variable length block codes is used to establish outer bounds to the performance for a given expected decoding time. The inner and the outer bounds match one another asymptotically and characterize the achievable region of rate-exponent vectors, completely. The single message message-wise unequal error protection problem for variable length block codes with feedback is also solved as a necessary step on the way.Comment: 41 pages, 3 figure

Exponential bounds on error probability with Feedback

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 95-97).Feedback is useful in memoryless channels for decreasing complexity and increasing reliability; the capacity of the memoryless channels, however, can not be increased by feedback. For fixed length block codes even the decay rate of error probability with block length does not increase with feedback for most channel models. Consequently for making the physical layer more reliable for higher layers one needs go beyond the framework of fixed length block codes and consider relaxations like variable-length coding, error- erasure decoding. We strengthen and quantify this observation by investigating three problems. 1. Error-Erasure Decoding for Fixed-Length Block Codes with Feedback: Error-erasure codes with communication and control phases, introduced by Yamamoto and Itoh, are building blocks for optimal variable-length block codes. We improve their performance by changing the decoding scheme and tuning the durations of the phases, and establish inner bounds to the tradeoff between error exponent, erasure exponent and rate. We bound the loss of performance due to the encoding scheme of Yamamoto-Itoh from above by deriving outer bounds to the tradeoff between error exponent, erasure exponent and rate both with and without feedback. We also consider the zero error codes with erasures and establish inner and outer bounds to the optimal erasure exponent of zero error codes. In addition we present a proof of the long known fact that, the error exponent tradeoff between two messages is not improved with feedback. 2. Unequal Error Protection for Variable-Length Block Codes with Feedback: We use Kudrayashov's idea of implicit confirmations and explicit rejections in the framework of unequal error protection to establish inner bounds to the achievable pairs of rate vectors and error exponent vectors. Then we derive an outer bound that matches the inner bound using a new bounding technique. As a result we characterize the region of achievable rate vector and error exponent vector pairs for bit-wise unequal error protection problem for variable-length block codes with feedback. Furthermore we consider the single message message-wise unequal error protection problem and determine an analytical expression for the missed detection exponent in terms of rate and error exponent, for variable-length block codes with feedback. 3. Feedback Encoding Schemes for Fixed-Length Block Codes: We modify the analysis technique of Gallager to bound the error probability of feedback encoding schemes. Using the encoding schemes suggested by Zigangirov, D'yachkov and Burnashev we recover or improve all previously known lower bounds on the error exponents of fixedlength block codes.by Bariş Nakiboḡlu.Ph.D

Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection.Comment: To appear in IEEE Transactions on Information Theor

The AWGN Red Alert Problem

Consider the following unequal error protection scenario. One special message, dubbed the "red alert" message, is required to have an extremely small probability of missed detection. The remainder of the messages must keep their average probability of error and probability of false alarm below a certain threshold. The goal then is to design a codebook that maximizes the error exponent of the red alert message while ensuring that the average probability of error and probability of false alarm go to zero as the blocklength goes to infinity. This red alert exponent has previously been characterized for discrete memoryless channels. This paper completely characterizes the optimal red alert exponent for additive white Gaussian noise channels with block power constraints.Comment: 13 pages, 10 figures, To appear in IEEE Transactions on Information Theor

Turbo-Detected Unequal Error Protection Irregular Convolutional Codes Designed for the Wideband Advanced Multirate Speech Codec

Abstract—since the different bits of multimedia information, such as speech and video, have different error sensitivity, efficient unequalprotection channel coding schemes have to be used to ensure that the perceptually more important bits benefit from more powerful protection. Furthermore, in the context of turbo detection the channel codes should also match the characteristics of the channel for the sake of attaining a good convergence performance. In this paper, we address this design dilemma by using irregular convolutional codes (IRCCs) which constitute a family of different-rate subcodes. we benefit from the high design flexibility of IRCCs and hence excellent convergence properties are maintained while having unequal error protection capabilities matched to the requirements of the source. An EXIT chart based design procedure is proposed and used in the context of protecting the different-sensitivity speech bits of the wideband AMR speech codec. As a benefit, the unequalprotection system using IRCCs exhibits an SNR advantage of about 0.4dB over the equal-protection system employing regular convolutional codes, when communicating over a Gaussian channel

On BICM receivers for TCM transmission

Recent results have shown that the performance of bit-interleaved coded modulation (BICM) using convolutional codes in nonfading channels can be significantly improved when the interleaver takes a trivial form (BICM-T), i.e., when it does not interleave the bits at all. In this paper, we give a formal explanation for these results and show that BICM-T is in fact the combination of a TCM transmitter and a BICM receiver. To predict the performance of BICM-T, a new type of distance spectrum for convolutional codes is introduced, analytical bounds based on this spectrum are developed, and asymptotic approximations are also presented. It is shown that the minimum distance of the code is not the relevant optimization criterion for BICM-T. Optimal convolutional codes for different constrain lengths are tabulated and asymptotic gains of about 2 dB are obtained. These gains are found to be the same as those obtained by Ungerboeck's one-dimensional trellis coded modulation (1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be asymptotically as good as 1D-TCM.Comment: Submitted to the IEEE Transactions on Communication

Design Of Fountain Codes With Error Control

This thesis is focused on providing unequal error protection (uep) to two disjoint sources which are communicating to a comdestination via a comrelay by using distributed lt codes over a binary erasure channel (bec), and designing fountain codes with error control property by integrating lt codes with turbo codes over a binary input additive white gaussian noise (bi-awgn) channel. A simple yet efficient technique for decomposing the rsd into two entirely different degree distributions is developed and presented in this thesis. These two distributions are used to encode data symbols at the sources and the encoded symbols from the sources are selectively xored at the relay based on a suitable relay operation before the combined codeword is transmitted to the destination. By doing so, it is shown that the uep can be provided to these sources. The performance of lt codes over the awgn channel is well studied and presented in this thesis which indicates that these codes have weak error correction ability over the channel. But, errors introduced into individual symbols during the transmission of information over noisy channels need correction by some error correcting codes. Since it is found that lt codes alone are weak at correcting those errors, lt codes are integrated with turbo codes which are good error correcting codes. Therefore, the source data (symbols) are at first turbo encoded and then lt encoded and transmitted over the awgn channel. When the corrupted encoded symbols are received at receiver, lt decoding is conducted folloby turbo decoding. The overall performance of the integrated system is studied and presented in this thesis, which suggests that the errors left after lt decoding can be corrected to some extent by turbo decoder